The deterministic robust estimation problem is formulated in the discrete-time case as a zero-sum two person difference game, in which a statistician plays against nature. The statistician tries to estimate a linear combination of the states of an uncertain linear system, which is driven by nature. Saddle-point strategies for the statistician in the above game are difficult to find. A suboptimal strategy is, therefore, considered which guarantees an H∞ performance bound on the estimation error. Different patterns of the information that is available to the statistician are treated, and the corresponding fixed-point, fixed-lag, and fixed-interval smoothing strategies are derived